Based on the abstract, general style of mathematical exposition favored by research mathematicians, its goal was to teach students not just to manipulate numbers and formulas, but to grasp the underlying mathematical concepts. The result, at least at first, was a great deal of confusion among teachers, students, and parents. Since then, the negative aspects of "new math" have been eliminated and its positive elements assimilated into classroom instruction.In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts underlying "new math": groups, sets, subsets, topology, Boolean algebra, and more. According to Professor Stewart, an understanding of these concepts offers the best route to grasping the true nature of mathematics, in particular the power, beauty, and utility of pure mathematics. No advanced mathematical background is needed (a smattering of algebra, geometry, and trigonometry is helpful) to follow the author's lucid and thought-provoking discussions of such topics as functions, symmetry, axiomatics, counting, topology, hyperspace, linear algebra, real analysis, probability, computers, applications of modern mathematics, and much more.By the time readers have finished this book, they'll have a much clearer grasp of how modern mathematicians look at figures, functions, and formulas and how a firm grasp of the ideas underlying "new math" leads toward a genuine comprehension of the nature of mathematics itself.

    This book provides a modern introduction to the main principles that are foundational to thermal physics, thermodynamics and statistical mechanics. The key concepts are carefully presented in a clear way, and new ideas are illustrated with copious worked examples as well as a description of the historical background to their discovery. Applications are presented to subjects as diverse as stellar astrophysics, information and communication theory, condensed matter physics and climate change. Each chapter concludes with detailed exercises.

    Indeed, numbers are part of every discipline in the sciences and the arts.With 350 illustrations, including diagrams, photographs and computer imagery, the book chronicles the centuries-long search for the meaning of numbers by famous and lesser-known mathematicians, and explains the puzzling aspects of the mathematical world. Topics include:The earliest ideas of numbers and counting Patterns, logic, calculating Natural, perfect, amicable and prime numbers Numerology, the power of numbers, superstition The computer, the Enigma Code Infinity, the speed of light, relativity Complex numbers The Big Bang and Chaos theories The Philosopher's Stone. The Book of Numbers shows enthusiastically that numbers are neither boring nor dull but rather involve intriguing connections, rivalries, secret documents and even mysterious deaths.

    

    A wealth of accompanying figures and exercises illustrate and develop the material in more depth. They describe what a quantum computer is, how it can be used to solve problems faster than familiar "classical" computers, and the real-world implementation of quantum computers. Their book concludes with an explanation of how quantum states can be used to perform remarkable feats of communication, and of how it is possible to protect quantum states against the effects of noise.

    It provides a simple, thorough survey of elementary topics, starting with set theory and advancing to metric and topological spaces, connectedness, and compactness. 1975 edition.

    Clear Science Teaching to Set the Stage for an Awe-Inspiring Course Created for a lay audience and readily accessible, in this course science always takes precedence over drama. The lectures are certainly entertaining, often funny, even awe-inspiring at times, as befits the subject matter. Even though you will be entertained, you will be learning good science. Clear introductions to essential principles of physics support these lectures, including density, quantum theory, gravity, and the General Theory of Relativity. Professor Neil deGrasse Tyson also includes forays into disciplines such as chemistry and biology as needed to explain events in astronomy. For example, Dr. Tyson begins one lecture at a point 13 billion years ago, when all space, matter, and energy in the known universe were contained in a volume less than one-trillionth the size of a pinpoint-about the size of a single atom. By the time he finishes, the cosmos has been stretched, the planets and our Earth formed, and 70 percent of existing Earth species have been wiped out by a gigantic asteroidclearing the way for the evolution of humanity. Along the way he has touched on Einstein's famous equation, E=mc2; on the four forces that were once unified in the early cosmos in a way physicists are still trying to explain; and on the chemical enrichment of the universe by exploding supernovae, which give the universe its necessary supply of heavier elements including oxygen, nitrogen, iron and, most important, carbon. Carbon, we learn, is a "sticky" atom, capable of making more kinds of molecules than all other elements combined. It's the ideal element with which to experiment in the building of life forms and is, of course, the element responsible for the remarkable diversity of life, including us. As Dr. Tyson notes, we are made of stardust, just as the planets are. And he has created a course that explains exactly how that came to be, beginning with a grounding in the basic "machinery" of matter, forces, and energy that has been discovered on Earth and which also reveals itself throughout the universe. The Stark and Violent Beauty of the Universe With this basic foundation in place, explanations of cosmic events fall logically into place, and the realities of the universe-including its eventual demise-are revealed in stark and often violent beauty. You learn: how Saturn's rings were formed, and why they will eventually be lost why low-density conditions are necessary to produce the drama of the northern and southern auroras why even the most jagged and wild of the Earth's mountain ranges are, from a cosmic standpoint, really part of a perfectly smooth sphere how black holes are formed and the extraordinary way in which they can wreak havoc in the universe how asteroids moving through space represent threats of extraordinary consequence to Earth, no matter how long those threats may take to be realized why the seemingly infinite panorama of celestial bodies revealed by the Hubble Space Telescope's famous "Deep Field" so intrigued astronomers how astronomers actually look for new planets, why the odds seem overwhelmingly in favor of some kind of life out there, whether we ever make contact or not. Most important, none of these ideas are presented as isolated "space factoids" that serve no purpose but to entertain. They are there to illustrate and reinforce the key principles of physics and astrophysics that are continually being presented in this course. But the inclusion of real science doesn't prevent Dr. Tyson from having some fun, either. When it's time to show how a black hole might remove one from the universe, he leads you right up to the "event horizon" and slips you in-feet first. Since the event horizon represents the point within which nothing, not even light, can escape, you might think this is a bad idea. And you would be right. But as you plummet toward the "singularity" at the heart of the black hole, you will learn firsthand about the interesting effects of gravity truly unleashed, including what physicists refer to, with a straight face, as "spaghettification." (Actually, Professor Tyson recommends that you be sucked in to a large black hole rather than a small one. You'll still be spaghettified, but it won't happen as quickly.) But make no mistake: Dr. Tyson does not consider the cosmos a laughing matter, this kind of whimsical touch notwithstanding. In spite of his training, he remains, admittedly, still in awe of his subject. And he has created a course that might well produce the same feeling in you.

    Even after more than three centuries and the revolutions of Einsteinian relativity and quantum mechanics, Newtonian physics continues to account for many of the phenomena of the observed world, and Newtonian celestial dynamics is used to determine the orbits of our space vehicles.This completely new translation, the first in 270 years, is based on the third (1726) edition, the final revised version approved by Newton; it includes extracts from the earlier editions, corrects errors found in earlier versions, and replaces archaic English with contemporary prose and up-to-date mathematical forms. Newton's principles describe acceleration, deceleration, and inertial movement; fluid dynamics; and the motions of the earth, moon, planets, and comets. A great work in itself, the Principia also revolutionized the methods of scientific investigation. It set forth the fundamental three laws of motion and the law of universal gravity, the physical principles that account for the Copernican system of the world as emended by Kepler, thus effectively ending controversy concerning the Copernican planetary system.The illuminating Guide to the Principia by I. Bernard Cohen, along with his and Anne Whitman's translation, will make this preeminent work truly accessible for today's scientists, scholars, and students.

    Designed primarily for undergraduates, this self-help manual offers straightforward solutions to common problems and an overview of the diversity of writing tasks faced by professional biologists.

    To love and loathe the fox is a British condition."The fox is our apex predator, our most beautiful and clever killer. We have witnessed its wild touch, watched it slink by bins at night and been chilled by its high-pitched scream. And yet we long to stroke the tumbling cubs outside their tunnel homes and watch the vixen stalk the cornfield.There is something about foxes. They captivate us like no other species.Exploring a long and sometimes complicated relationship, The Wild Life of the Fox captures our love – and sometimes loathing – of this magnificent creature in vivid detail and lyrical prose.

    Using video links, IP Factly's Amazing Animal series has been designed to encourage and bolster independent reading. The animals are accompanied by pictures and facts plus video links so children can see the animals and how they behave.

    It resurrects from the vaults of neglect the polymath Jerome Cardano, a Milanese of the sixteenth century. Who is he? A gambler and blasphemer, inventor and chancer, plagued by demons and anxieties, astrologer to kings, emperors and popes. This stubborn and unworldly man was the son of a lawyer and a brothel keeper, but also a gifted physician and the unacknowledged discoverer of the mathematical foundations of quantum physics. That is the argument of this charming and intoxicatingly clever book, which is truly original in its style, and in the manner of the modernists embodies in its very form its theories about the world.'The Quantum Astrologer’s Handbook' is a science book with the panache of a novel, for readers of Carlo Rovelli or Umberto Eco. It is a work of and about genius.

    Now renewables are overtaking fossil fuels, with wind and solar energy becoming cheaper and more competitive every year. Growth in renewable energy will further accelerate as electric vehicles become less expensive than traditional automobiles. Understanding the implications of the energy transition will prepare us for the many changes ahead.This book is a primer for readers of all levels on the coming energy transition and its global consequences. Bruce Usher provides a concise yet comprehensive explanation for the extraordinary growth in wind and solar energy; the trajectory of the transition from fossil fuels to renewables; and the implications for industries, countries, and the climate. Written in a straightforward style with easy-to-understand visual aids, the book illuminates the strengths and weaknesses of renewable energy based on business fundamentals and analysis of the economic forces that have given renewables a tailwind. Usher dissects the winners and losers, illustrating how governments and businesses with a far-sighted approach will reap long-term benefits while others will trail behind. Alongside the business and finance case for renewable energy, he provides a timely illustration of the threat of catastrophic climate change and the perils of delay. A short and powerful guide to our energy present and future, this book makes it clear that, from both economic and environmental perspectives, there is no time to lose.

    The book begins with relevant scientific fundamentals and progresses through an exploration of the solar system, stars, galaxies, and cosmology. The Astronomy textbook builds student understanding through the use of relevant analogies, clear and non-technical explanations, and rich illustrations. Mathematics is included in a flexible manner to meet the needs of individual instructors.

    From Hesiod's Chaos, described in his poem about the origins of the Greek gods, Theogony, to today's mind-bending theories of the multiverse, humans have been consumed by the relentless pursuit of an answer to one awe inspiring question: What exactly happened during those first moments?Guido Tonelli, the acclaimed, award-winning particle physicist and a central figure in the discovery of the Higgs boson (the "God particle"), reveals the extraordinary story of our genesis--from the origins of the universe, to the emergence of life on Earth, to the birth of human language with its power to describe the world. Evoking the seven days of biblical creation, Tonelli takes us on a brisk, lively tour through the evolution of our cosmos and considers the incredible challenges scientists face in exploring its mysteries. Genesis both explains the fundamental physics of our universe and marvels at the profound wonder of our existence.